Why is it so hard for people to understand this. In some games there is no variance within the game. You have all the information on the table (chess) which you can use to make the perfect decision, therefore games like Chess or tic-tac-toe have no variance. There is variance in the RESULTS, which is a completely different issue. In almost all games there are elements that you cannot control (poker quite obvious, any game played with dice etc...)

Chess is just a very complicated tic-tac-toe in the sense that if played perfectly the outcome is fixed. I guess it's a tie as well every single time if played perfect, right? or is white going to win it, I dont know. Doesnt really matter though.

There seems to be variance in some games is because humans are not perfect. If one day some geniuses can build a computer which makes no mistakes in chess, we can watch them play a million games and the result of each game is going to be the same . Much like computers playing tic-tac-toe. (Now someone is going to ask is every single game going to be the copy of the previous one. I dont know, but I doubt it. There are probably spots where at least 2 moves are equally good, in which case the games are not going to be copies of eachothers, but this is not a proof of variance, the result of the game is still going to be the same. If the games vary it's not a proof of anything. Tic-tac-toe games vary, but the results is always the same)

It baffles my mind how people dont get this, amazing really.. :S

Folding would still be a decision by the players. Like I said before, you cannot calculate variance without considering each player's strategy.

The definition on wikipedia ia what variance means. You cannot dismiss it and invent your own definition of it. That's not how it works.

Karganeth it's no use to waste so much energy trying to explain this, if they haven't gotten it yet, I doubt they ever will.

I am wondering the following: I think it is pretty much shown now that the game of chess itself is not a source of variance.
However, how is it from the chess player's perspective? Let's say that you are a really dumb player, playing another really dumb player. Basically you are randomly moving around your pieces and so is your opponent. After, let's say, 30 moves, you happen to hold a much better position than your opponent, and even with your very limited skills you manage to win from this position.
Now in this case, where the first 30 moves were basically randomly selected by both you and your opponent, I think you can argue that you have pretty much won through sheer luck.
Of course this is very extreme, but in more realistic cases you do not oversee the consequences of all of your moves, and a lot of times you more or less randomly select one move from a subset of moves, and sometimes this one just happens to be a great move. So in selecting this move there was some skill involved, but also some pure randomness.

So I'm not arguing that this is the result of the game of chess. I agree that in principle the game itself causes no variance or randomness at all. I'm just wondering whether in real life with all chess players being more or less unable to fully understand the consequences of their moves, isn't there in fact a big factor of luck/randomness.
So wouldn't this lead to the conclusion that in real life you might lose a game of chess although you are really the better player but you just happened to be unlucky? It could even be that in that game, your thought processes and strategic decisions were better, but the random fluctuations in chosing your moves worked out against you?

Yes there would be variance in your result. Just because there isn't variance in the answer, doesn't mean there's no variance. The person has a value that is different from the mean, inserts variance into this game.

Your example leaves things up to debate though. Like much of everything in this damn topic, a huge difference in semantics. He could've meant 1+1 = 2, but his wrist was sprained and he accidentally wrote a 3, which wouldn't insert variance into the equation of his conclusion to the answer. Just to his ability to record it.

The people in this thread who are arguing that there is no variance in the game of chess are actually making a very different point; that there is no randomness inherent in the rules of chess, while there is in poker. This is blatently obvious and doesn't even need to be argued. Arguing that there is no variance in chess is something quite different.

It is obvious that there is variance in chess if you know the following things:

1. What variance actually means.

You don't even need to know what the rules to chess are to see there is variance in the results - you only need to know that the weaker player can beat stronger players (and of course, you know need to know what 'variance' actually means )

surely the better player is the one who makes better use of the perfect information available in a game of chess to win any given chess match

The better player is generally regarded as the one expected (in the mathematical sense) to have a better result in a game - the ELO system that awards grades is just a statistical tool designed to approximate this expectation based on previous results. It usually gives a pretty good estimate, although lots of factors mean it is obviously not perfect.

I have explained this in an earlier post. Since you have a better understanding of the game than your opponent, you are actually gambling less than him and have a good edge on him. Your moves are much more calculated and accurate compared to his more random pushes so it's more likely you'd win. It's kinda like shoving your 2 pair on the flop against a flush draw. There is a good chance he can win, but surely your two pair is the better hand and is more likely to hold up. In the long run you will certainly win more games than the weaker player.

Yes you could say you were unlucky when you lost to the weaker player, but you still have to remember that it's still your own fault. He beat you by putting you into a position you didn't fully understand and blundered, when you should know the position if you are a chess pro. Sure he might have less knowledge than you overall, but he does know this one area that you should know. It's up to you to learn from it so you can improve and be closer to playing perfect.

Right. There is really no convincing you. Have it your way. There is no variance without considering each player's strategy.

I don't want to ever hear you complaining about suffering a bad beat or is running bad ever again. Since it is your strategy that affects the variance in the game, it is totally your fault that you got sucked out. If you adjusted your strategy accordingly you will never get sucked out, since as you say, the variance that caused you to get sucked out is caused by your current strategy. It's your fault when your all in with AA and got sucked out by KK, not variance within the game.

Right so what is the ELO rating of a perfect chess computer that has solved the game?

The problem here is that Karganeth and Seven are looking at variance at a statistical viewpoint solely without applying that knowledge. They probably took a statistics 101 course and spout out their textbook definitions without ever applying the knowledge.

Chess is not supposed to have variance. If there is variance it indicates imperfection, which means it isn't perfect pure chess that we are arguing about here.

Let's say you are building an aircraft wing that is supposed to be 20 meters long exactly. Any deviation from 20 meters is imperfect and will cause the aircraft to crash. Karganeth is assigned to tabulate all the lengths of the wings produced by the factory and determined that the mean length is 20 meters with a variance of 2. Now this will mean that the aircraft wings made are not all perfect and the factory manufacturing process is not perfect too. Corrections have to be made to the wings and manufacturing processes to ensure that future production will always produce 20m wings. This is because there is no variance in aircraft wing design and any variance is due to external fault that has to be corrected.

But Karganeth, being the mathematician he is, concluded that there is variance in aircraft wing lengths because his tabulated result shows a variance of 2. What he doesn't understand is that there is not supposed to be variance and his variance is a result of imperfect wings and manufacturing processes and not that the specfic aircraft wings will all have variance.

Now chess is supposed to be variance free. Any sign of variance indicates imperfection and shows that the players have areas in their game that can be corrected and improved on to be perfect. Of course no one is perfect and the human brain isn't even powerful enough to calculate chess all the way to be be perfect, and thus you will see variance in human play. Unless you are telling me Kasparov is perfect and there is nothing more he can do to improve his game. This does not mean computers will play with variance though...they will play perfect one day.

You would need results to calculate it, but I would guess it to be in the mid-3000s - there are extreme diminishing returns when playing players with a much lower ELO so it probably could not get much higher than that. ELO is just an estimation and does not work well with players of greatly different strength - it would be a fairly meaningless number in the case you mention.

Actually the computer's ELO rating will be infinite, since it is impossible to beat it. ELO gives an indication of relative player strength which you can use to calculate the probability of a player winning against another player. Since the perfect computer can never be beaten, its ELO will be infinite. And the rating will never drop since it will never lose.

This shows that with perfect play there can be no variance and there will be no sense using statistical models to calculate its play. This is because CHESS HAS NO VARIANCE.

To clarify: I am not saying that variance is 0, I am saying that variance in a game cannot be calculated without there being decisions from players.

You seem to be confused about variance. It doesn't matter if he sucks out or not, the variance is the same in both situations. Variance describes the distribution. It is concerned with all potential results. The actual results don't affect variance.

Clearly, chess has no variance if the same moves are played by both players each time. This is trivial and uninteresting.

It's also obvious that the RESULTS of chess games DO HAVE VARIANCE because the same player doesn't win every time.

A more interesting question is to explore the possibility of luck within chess as experienced by two human players playing with a time limit. This, afterall is the way the game is played. The luck element in chess is the unforseen consequences of moves.

Pick any move in the opening or middle game. Say black takes a bishop and white decides to recapture with a pawn rather than with the knight. While this may have some immediate tactical significance, the impact that this choice of recapture will have say 20 moves down the line is unforseen by both players and could turn out to be a big factor. Maybe the pawn will block white's own attack or maybe it will be a strong support point for a knight or maybe white will expend too much energy trying to protect it later or whatever. Most moves have consequences that NEITHER player is able to calculate within the allotted time.

These unforseen consequences make up the luck element in chess and contribute to variance in results.

I agree with the second point but not the first.

Just because the same player doesnt win every time does not explain varience. The varience in the result would be the distance from the expected outcomes (assuming we could quantify how often one player should beat the other).

Your second point is interesting. I agree that the luck element in chess is "the unforseen consequences of moves" and this in itself does not equate to varience. But as it impacts the results of the game, then it could be considered part of the varience of the results (if we could quantify how often one player "should" beat the other)

I can accept that and I totally agree with you. Whether any entity will ever be able to play perfect chess is a different matter; in theory it is possible.

fyp

Well know that computers can already play tic-tac-toe, connect 4 and checkers and a whole slew of other games perfectly. It only requires a slight stretch of imagination to assume that they can play chess perfectly eventually as well.

You say you calculate your variance through your results, and then now you say your actual results don't affect variance?

You are all over the place man. Every post you made is fraught with contradictions. If anything has variance it is your logic skills.

Try answering to all the points brought up instead of repeating the same points that are refuted again and again. Is there supposed to be variance in standard coke bottle sizes if your factory produced a 2.1 L bottle followed by a 1.8L bottle?

Where did I say that?

You don't understand what variance is and you continue to believe it's ok to invent your own definition.

They would prefer the variance to be 0 but in reality it is not. The probabilities of coke bottle sizes other than what they aim for is not 0. I'm not really sure what you're getting at.

This is, of course, foolish, and an assertion virtually all chess players would deny. There is a reason the elite chess players of the world are notorious for being meticulous about the circumstances under which they play (cf. Fischer as a superb example). The qualification I would agree with is the better chess player is the one who, under equal conditions to his opponent, is superior in skill. There is a long list of necessities a chess player desires to ensure he is on equal ground to his opponent. In a game as intricate and complicated as chess, not having one's regular cup of coffee is enough variance to virtually guarantee a loss from a player who's extremely close in talent to another (but better). Other examples of stated necessities have been certain lighting conditions, room temperature, geographical location, time of the day, number of days notice, etc. Basically, each player needs to be able to concentrate fully, and each individual has their own view of what they need for that to happen. This is not to say a better chess player will be able to concentrate better under x, y, z conditions, but it is true that certain x factors can occur which alter one player's concentration to the point where they cannot perform to their potential.

As a simple refutation, if a player's wife dies the day of a match, it is not necessarily true that the better player will win. Certainly the widow(er) may lose because of the variance of having a loved one die so close to the match. The widow(er) might be the better player and might handle the loss better (in terms of playing the match) than his/her opponent would have, but he/she still might lose. This is just one example of variance that can occur in a "purely" skill game.

I read a book where one IM laughed at the notion that there's no variance in chess, and stated something to the effect of there being as much variance in chess as in [something like gambling]. Just as in poker, sometimes a person is one their "A-game", and sometimes not, the same happens in chess. I've lost to many players I'm much better than. There are so many factors involved, all that can be said is the player who plays better that game or match will win in chess (whereas this is not necessarily true in poker). It cannot be said the better player will win. This fact is exemplified in the fight game as well (MMA) when the loser will say, "I give him props, he was the better fighter tonight", or "he fought better than me tonight" -- they are saying the better performer won, not the better fighter. And that could very well be the case, for example a very, very rare series of physical events could have exchanged which lead to a situation that is more familiar to the overall vastly inferior fighter which allowed him to win, or even a lack of skill can sometimes result in an accidental advantage. It is much more complex than you make it out to be.

I maintain that poker is a 100% skill game with (theoretical) short-term variance. The better player will always win in the theoretical long run, once all or enough variance has evened out.

Not exactly true. Your rating drops every time you give up a draw to a lower rated player, and I'm sure there are humans who could manage an occasional draw against a perfect computer.

Also, it is not known whether chess is a draw, a win for white, or a win for black. If chess isn't a draw then a perfect computer's result, at least when paired with another perfect computer, would depend solely on its color.

Finally, if it only played other perfect computers, then its rating would converge to the average rating of its opponents. If they all only played each other, their rating would be whatever they were seeded with when they began play. I think 1500 was what Elo started with.

But, yeah. If your point is that a perfect chess computer's results would have zero variance while a perfect poker computer's results would have non-zero variance, I agree. The two games are fundamentally different.

The claims in this thread that there is variance in chess because the players are imperfect, or because a meteor might strike the stronger opponent and cause him to forfeit, miss the point. The point is this: the rules of poker give rise to variance no matter how the players play; the rules of chess do not.

I don't see how anyone can argue against this, but here we are.

I think it's incredibly lame to give the perfect computer a provisional rating and have it work its way up. A few wins against the world champion and it's rating will be 3000-4000 already. What's the point?

And I think it's a laugh that humans can draw against the perfect computer. Right now rybka is owning grandmasters giving them white as well as a pawn advantage with additional thinking time. Compared to this, the perfect computer will never draw with a human. One or 2 suboptimal moves and you will be totally drawing dead against it